Merton model and Poisson process with Log Normal intensity function

TL;DR

This paper explores the connection between the Merton model with temporal correlation and Poisson processes with log-normal intensity, revealing phase transitions and applying the model to default portfolios for improved long-term predictions.

Contribution

It demonstrates that the Merton model converges to a Poisson process with log-normal intensity and links it to Hawkes processes, extending understanding of credit risk modeling.

Findings

The Merton model becomes a Poisson process with log-normal intensity in the limit.

The model exhibits a super-normal transition under power-law temporal correlation.

Power decay models outperform others in long-term default portfolio predictions.

Abstract

This study considers the Merton model with temporal correlation. We show the Merton model becomes Poisson process with the log-normal distributed intensity function in the limit. We discuss the relation between this model and Hawkes process. In this model we confirm the super-normal transition when the temporal correlation is power case. The phase transition is same as seen before the limit. We apply this model to the default portfolios and find that the power decay model provides better generalization performance for the long term data.